You make it sound like time labels like "23:59:58Z" can perform actions (e.g. to skip or "suppress").

I had to look it up: https://www.timeanddate.com/time/negative-leap-second.html . In proper words, the clock ("the one humanity agrees to use) would skip 23:59:59Z.

I wonder how much chaos a minute that only has 59 seconds would cause. Measurements would be off by that missing second (e.g. a pipeline delivering fuel at 60 liters/minute would surprisingly only have 59 liters in that minute..).